Permanent magnet electric machines in which one of a stator and rotor has permanent magnets (PMs) and the other has magnetic coils, employ waveform generators that rely on an input indicating the precise instantaneous position in order to work correctly. Incremental encoders, such as those that can indicate a relative displacement per interval of time such that a cumulative count can give a total displacement, can be used to track position over time. Incremental encoders are simple and relatively inexpensive, but do not provide an absolute position, which is information that is required to control many types of permanent magnet machines, particularly at startup. When a brushless DC motor starts, the initial position must be known. Currently, in the automotive industry, it is believed that resolvers are preferably used for the purpose of indicating rotor position. The resolver can indicate the absolute position of the rotor relative to the stator including an initial position. Other types of absolute position indicators are also known, such as absolute encoders which employ a variety of different electrical, optical, or mechanical principles.
The designs of certain types of resolvers are suitable for use in PM motors that have even numbers of pole pairs. The position indicated by a resolver indicates at least a unique driving state of the PM motor, even if it can be mapped to more than one rotor position as it can for an even pole-pair motor. This is because the even pole-pair motor have at least two rotor positions that are identical in terms of the optimal excitation signal required to drive them. However, when such a resolver is used for a motor with an odd number of pole pairs, each position indicated by the resolver maps to two distinct positions of the rotor that do not correspond to identical driving states. However, it may be desirable, for cost reasons for example, to use such a position indicator for the control of a permanent magnet machine with an odd number of pole pairs. For example, if the demand for such indicators is higher than for resolvers suitable for odd pole-pair motors, then the costs would tend to be lower. It would be desirable under such circumstances, to use the low-cost indicators in odd pole-pair motor to take advantage of the lower costs.